Hyperscript

Defects in Crystals

Preface

It has been my experience that folks who have no vices have
very few virtues

A. Lincoln

Defects in
crystals - are they of any relevance for life in general or
materials science in particular?

Lets see: Diamondsare crystals and, as we are told, they are
forever (a lie) and girls best friends (a lie, too, we (men) hope) - but if you
buy one, it is mostly the defects in this carbon crystal that determine how
much money you spent for a given size.

If you do not buy diamonds on a regular base, you
are still exposed to defects in crystals in many ways. However, you may not be
aware of this fact. So let's look at examples.

You are dealing with defects in crystals, whenever you

bent a piece of metal by applying
some force (e.g. when you wrap your car around a tree) and when you do not bent a piece of metal (e.g. when
you drive your car over a bridge that does not bent under the weight).

use any piece
of electronic hardware.

complain about the high costs of solar energy, or the low mileage (= miles per gallon) of your car.

This needs explaining.

First we have to realize that all
solid metals are crystals (like most other non-biological
substances), even though they don't look like it. The shape of some piece of
material does not necessarily say much about its atomic structure, and language
can be deceiving. What in daily life is called "crystal" is often the
exact opposite, namely amorphous glass.

Gemstones, which often are
crystals and look like it by assuming some
kind of geometric shape as, e.g. cubes, double pyramids etc., are very special crystals, called "single crystals".

This simple presentation does not
only illustrate rather clearly the concept of "crystals" but gives an
idea about defects in crystals as well.

The boundaries between the crystalline areas in
the left-hand figure, the "grains"of the crystal, are obviously
defects (appropriately termed "grain boundaries") in the regular
lattice of a crystal, because in these areas the regular structure of the
crystal lattice is disturbed. The atoms of the crystal are not were we would
expect to find them. More defects are shown; e.g. "wrong" atoms,
surplus atoms or missing atoms.

Metals, like practically all
crystalline materials found in nature (e.g., most minerals, ores or salt), are
poly-crystals full of defects. The same is true for most (but not all) man-made
crystals, in particular metals and alloys.

If we look at those technical
crystals, we find that a very large part of their interesting properties,
including in particular many of their mechanical properties as, e.g. hardness,
ductility, or brittleness, are controlled by the defects in their crystal
lattice. A perfect single crystal of some metal would be void of technical
interest, it would be rather useless. The metal industry (especially the
so-called "metal-bending industry") lives exclusively from the
manipulation of defects in the metals and alloys they use.

If you ever saw a smith doing its thing (remember
"Under a spreading chestnut
tree"), or at least saw a remotely natural performance of
Wagners
"Siegfried", you witnessed defect
manipulation. Lets see:

Siegfried forges his sword. First he pours the molten "steel" into a form,
he casts his sword. After cooling, he actually has
a sword. The sword, in principal, exists after solidification, and a chemist,
extracting a sample, would find a lot of iron (Fe), some carbon
(C) and traces of everything else.

Siefried, however, is not yet done, he commences
to forge his sword. He bangs it with a hammer,
heats it up again, thrusts it into cold water (or oil?) heats it up again and
bangs it up some more. Of course, he also does some magic (in the opera he does
some heavy singing instead), before he is satisfied with his sword. And every
smith in the world for the last 3000 or so years, has gone more or less
through the same procedures.

The chemist is puzzled. Analyzing a sword sample
after this rousing performance yields exactly the same result as before: the
composition of the sword material has not changed at all.

Siegfried, however, is not a chemist but a
material scientist. He knows that a freshly made sword is too soft or too
brittle, and might bend or break in fights with dragons and other evildoers.

After the sword has been properly forged,
however, it is strong and elastic, it will keep an edge and won't break - it is
now perfectly suited to kill dragons and people.

Nowadays we prefer to use cars or guns to kill
people.

But nothing has changed in principle. The car parts are still
forged or treated in some way to obtain the required properties - without
changing their composition. And we obtain the desired properties because by
forging we manipulate the crystal defects in the
steel, we introduce suitable defects in proper concentrations and
structures and get rid of others.

So much for metals. Looking at the
roots of the electronics and communications industry, we find semiconductor
technology. Inside an integrated circuit (IC), the mainstay of the industry, we
find a small Silicon (Si) crystal, a chip. The
Si crystal from which the IC is made, is an extremely perfect single crystal - in contrast to
metals. It was produced with an enormous amount of science, know-how, and
machinery, and it is the most perfect object that can be found on this side of
Pluto. It is also quite expensive.

Without a rather perfect Si
crystal as starting material, advanced ICs and other semiconductor
devices simply would not work. A transistor, the basic unit of a circuit,
consists of small areas of the silicon where specific defects have been
deliberately introduced (and others kept out) - again we are manipulating
defects to make a product.

We are even using some specific
defects, to get other defects to the places in the crystal where we want to
have them. Being done, we have to get rid of our helper defects - you get a
feeling for the complexity of the process.

There is, however, a major difference
between forging a sword and making a chip:

Our smithies may have applied material science -
but they certainly didn't know that! Until about 1930, nobody knew
exactly what happened during forging or why it worked, but that did not keep
our forefathers from making battleships, complicated watches, Eiffel towers and
railways.

Metallurgy was an empirical science; the best materials, processes,
and procedures were essentially found by trial and error through the
millenniums. Of course, hard sciences like thermodynamics and analytical
chemistry helped in the 19th century, but the basic theory of plastic
deformation came long after the products.

Chips, on the other hand, are
products of theory. Humans with 19th
century knowledge could tinker around forever without ever coming close to
making a transistor.

Solid state electronics, which includes
everything made from Si, GaAs and the like, may be seen as the
start of active materials science (as
opposed to material knowledge), where
understanding your materials and your product comes before making it. And understanding your materials
means mostly understanding its defects, too.

But coming back to the questions
asked above: How are the high costs of solar
energy or the low mileage of your car related to defects? Easy:

Cheap Silicon is cheap because it
contains many crystal defects - and makes lousy solar cells. Good solar cells
need expensive Si with few defects - or cheap Si with
"optimized" defects. How to optimize defects in cheap Si by
some process akin to forging brittle iron into tough steel, is what materials
scientists do in their research labs.

What do you need for the 100 miles per
gallon car? Very useful would be a drastically reduced weight without loosing
size, stability and comfort. So take Aluminum, or even better, Magnesium for
making the body and other components.

Unfortunately, these metals are meeting most of
the 50 or so requirements for structural car materials, but not all.
Mg, for example, is prone to corrode too quickly (a little bit of
corrosion is fine for selling new cars). Again, this is a property that can be
tailored to some extent by introducing the right defects into the Mg
crystal - but so far nobody knows how to do this without degrading some of the
other properties or making it too expensive.

Of course, your mileage goes up, too, if the
engine could work at higher temperatures and therefore with higher efficiency.
But conventional metals have been pushed to their extremes, what we need to do
now is to look for e.g. intermetallic compounds or ceramics that have the
desired properties and are still affordable. Again, we are looking for the
right kind of defect engineering as soon as we have selected a likely base
material.

The list could be extended, but by now you get the
idea why understanding and using defects in crystals leads you to the roots of
human civilization.

To be sure, much has been achieved in the past, and much will
be done in the future, by persons who do not know a lot about defects, but know their
materials instead.

In the industrial practice you don't go to the roots, you
start at a higher level. Hardly anybody among the practitioners of chip
production worries about the defect situation in the Si crystals - you
know that somebody else does and that you can buy near-perfect Silicon. You do
your diffusion processes on the base of phenomenological theories or by using
software packages that simulate whatever you want. But some are left who worry,
and without them the others couldn't work.

The short history of Si technology and thus
of microelectronics at large nicely illustrates this point.

Hardly anybody knows that the detailed mechanisms of the
diffusion of substitutional elements - the mainstay of Si processes -
are far less understood than in most other crystals. The first ICs were
made with empirical knowlegde and a totally wrong theoretical picture of the
atomic processes. Those ICs, however, worked anyway.

But todays ICs wouldn't be here without the results of
much research conducted in the meantime, because the extremely fine structures
encountered today would have been beyond the power of simple empirical
equations.

Some materials scientists thus should know the
basics about defects in crystals. This is knowledge that will not change much
in the times to come and that always will help to understand what is going on
an atomic scales when anything changes in crystals. This course tries to
present that knowledge in a short and much abbreviated way. It covers all basic
kinds of defects in one semester, which is
a bit unusual. We will look at

Experimental ways to observe defects and to
measure defect properties.

In dealing with defects in crystals, we always
must visualize some disorder in space, which for most people is not an easy
thing to do. Whereas some scientists are perfectly happy with abstract
mathematical description of objects including defects, most of us must have
some spatial image of what is discussed to be able to grasp what is going on.

Visualization therefore is a must and this is where multimedia
techniques may come into their own. Look at the schematic drawing of a
dislocation below - can you see the dislocation?

You sure could when you would be able to rotate the image so
you can view the dislocation from various angles, and you sure learn more by
doing this compared to looking at a drawing that only shows one perspective
that somebody else picked for you.

Perspective view of the most
simple dislocation in a cubic lattice. The dislocation line has been marked by differently
colored spheres.

In view of this, the course
"Defects in Crystals" was used as a vehicle to try out for the
first time the possibilities of the new media in teaching a non trivial
subject. A "Hyperscript" was
collated on a "lecture note base", i.e. there are no long verbal
descriptions.

This hyperscript is
an English version of the original German hyperscript, but includes
advancements made in the meantime; it is also formatted in a slightly different
(and hopefully) improved way.

It is now the
"real" thing; the German version, while still kept, will no longer be
updated.

The hyperscript consists of 5 major
parallel "strings" which are:

Basics
Here you will find some basic background knowledge about subjects that should
be known, but can bear to be repeated.

Backbone 1
This is the main part - it would be the "book" in a conventional
format.

Backbone 2
Additional "chapters of the book" that are not in the top priority of
the course, but may be used on occasions.

Illustrations
All those pictures, graphs, movies and other materials that would drive your
book editor up the wall if you would try to include it in a conventional
book.

Exercises
Typical exercise questions together with typical solutions

Advanced
Everything you do not have to know, but may take an interest in. This may
include hard-core science or interesting recent developments in the field, but
also anecdotes or historical notes.

I sincerely believe that hyperscripts will replace
classical text books in years to come. But I also believe that nobody
(including myself) knows at present how to produce the perfect, defect-free
hyperscript. Only time will tell.

Being willing to learn, I do invite comments and suggestion
for improvements. Please get in touch via e-mail:

Wagner got it totally wrong! Siegfried does not
pour anything - simply because he could not melt iron or steel (nor could
anybody else); his fire was simply not hot enough.

That he (and other smiths, too) nevertheless could
obtain iron and forge a sword for more than 2000 years before melting it became
possible, is one of the less well known marvels of ancient history. A glimpse
of the underlying technology can be obtained by jumping to "history of steel"
or to "Damascene
technique in Metal Working"; from there you may enter the fascinating
world of magical swords or otherwise remarkable issues of metal working (and
thus defect manipulations).